Numerical investigation of ship motions in cross waves using CFD
Introduction
Ship seakeeping performance has long been an important research topic in the field of naval architecture and ocean engineering. Almost all the existing numerical and experimental methods have focused on investigating ship motions in (2D) uni-directional regular or irregular waves. Real ships operate in ocean waves during their whole life period. Realistic ocean waves are however (3D) short-crested or multi-directional with wave components propagating in different directions. It is known that the directional spreading of wave has a significant influence on the loads and motions experienced by ship (Nwogu, 1989). Therefore, an in-depth understanding of ship motion behavior in multi-directional waves is fundamental for accurate prediction of real ships’ motion behavior in realistic ocean waves.
The initial studies on irregular waves have considered single wave systems that are properly modelled by wave spectra. However, many sea states found at sea are more complex and they can be composed by one spectrum representing the local wind sea and a second one representing a swell system that is arriving from a storm generated a distance away. This creates a double peak spectrum (Guedes Soares, 1984), which was shown to be relatively frequent at sea (Lucas et al., 2011). The wave systems can come from the same direction, but most often they come from different directions. The influence of wave systems coming from different directions and having different directional spreading has been studied by Teixeira and Guedes Soares (2009), who looked at the long term and extreme wave loads in those conditions and their influence to ship structural reliability.
When the wind or swell waves come from two orthogonal directions meeting in a common sea area, then cross waves (also called square waves) will be generated. This is a situation not much studied but which occurs in some cases as shown in Fig. 1,1 ,2,3. The cross waves may pose a threat to the navigational safety of passing ships. For example, ship may experience large amplitude roll–pitch coupled motion and this will further result in green water on deck (Fonseca and Guedes Soares, 2005), slamming event (Wang et al., 2016), asymmetrical water entry (Wang and Guedes Soares, 2013) and structural strength issues (Corak et al., 2018). This paper focuses on investigating ship motion in the most classical and representative multi-directional wave case, i.e. in orthogonal cross-waves. This study also has practical application values in evaluating ship navigational safety when subject to cross-seas and could provide some useful operational guidance for captains.
Investigations of the hydrodynamic behavior of fixed marine structure interacting with multi-directional wave can be found in some works. Xu et al. (2019) investigated the wave loads on a vertically fixed cylinder in multi-directional random wave by desingularized boundary integral equation method (DBIEM). Ji et al. (2015) investigated the wave loads on an array of bottom-mounted vertical cylinders in multi-directional random wave both theoretically and experimentally. Song and Tao (2007) investigated the general 3D short-crested wave interaction with a concentric two-cylinder system by potential flow theory. Wang (2006) studied the wave loads on a semicircular breakwater in 2D and 3D random waves both theoretically and experimentally. The methods in the literature are not applicable for the estimation of ship motion since 3D radiation is not considered.
Some existing publications have focused on investigating the motion behavior of ships or floating structures in short-crested waves. The majority of the related works were conducted by potential flow theory or model tests. Jiao et al. (2019) investigated ship motions and loads in different short-crested wave fields by 2D spectral analysis method in combination with frequency-domain hydrodynamic theory and the influence of wave directionality on ship motion and load responses has also been systemically analyzed. Jiao et al. (2018) conducted large-scale model seakeeping measurements in coastal waves in order to obtain more realistic ship motion responses in short-crested sea waves. Renaud et al. (2008) studied the second-order wave loads on an LNG carrier in mono-chromatic and bi-chromatic cross waves by HydroSTAR software and tank model test. Zheng et al. (2009) investigated the difference of ship motion responses in long-crested and short-crested irregular waves by 3D potential flow theory and tank model test.
Till now, different numerical methods have been developed in a large number of studies to predict wave-induced ship motion responses in regular waves (Hirdaris et al., 2014, 2016; Rajendran et al., 2016). Potential flow theory, ranging from simple 2D strip theory (Salvesen et al., 1970) to 3D panel method (Singh and Sen, 2007) also with different levels of nonlinearity taken into consideration, has been widely used for several decades due to their obvious advantages such as high computational efficiency. Calculations in frequency domain are faster and are useful in providing preliminary insights in the early design of ships (Cakici and Aydin, 2014). A ship in rough weather is subjected to various nonlinearities due to large amplitude motion and complex body geometry, which requires investigations in time domain to model them accurately (Sen, 2002; Guedes Soares et al., 2008). Watanabe and Guedes Soares (1999) conducted a benchmark study by comparing different nonlinear time domain codes for evaluating wave-induced vertical bending moments of ships.
Some complex flow physics and phenomena such as flow separation, fluid splash and viscous effects cannot be reproduced in the framework of potential flow theory. With the development of computer science and technology, Computational Fluid Dynamics (CFD) methods making use of Reynolds Averaged Navier–Stokes (RANS) equations are becoming increasingly popular and mature, which has the potential of assisting in ship design and evaluation. Some strongly nonlinear issues that caused by high forward speed, large amplitude motions and violent free surface flow can be well addressed by CFD method. Deng et al. (2019) investigated added resistance and motion response of a trimaran in head regular waves based on RANS method. Javanmardi et al. (2008) developed a CFD code to investigate the hydrodynamic resistance and maneuvering of a trimaran with Wigley body form in the conditions of different outrigger positions. Bhushan et al. (2009) conducted model and full-scale unsteady RANS simulations of ship resistance, powering, seakeeping and maneuvering. Islam and Guedes Soares (2019) studied the effect of trim on container ship resistance at different ship speeds and drafts. A CFD technique has turned out to be reliable in simulating wave-induced ship motions in uni-directional wave (Tezdogan et al., 2016).
Although tremendous advances have been made in the CFD simulations of ship motion responses in uni-directional wave, investigations of ship motion in multi-directional wave that simulated by CFD are rarely seen. Methods of multi-directional wave simulation by CFD tools have been reported by some researchers. Wang et al. (2018a) simulated directional irregular waves by open-source CFD wave model REEF3D. Park et al. (2004) reproduced fully nonlinear multi-directional waves by use of a viscous 3D numerical wave tank simulation technique and calculated the hydrodynamic forces on an advancing ship. Cao and Wan (2014) developed a three-dimensional multi-directional nonlinear numerical wave tank by using the two-phase hydrodynamic flow solver Naoe-FOAM-SJTU which was in-house developed based on the open source toolbox OpenFOAM. Wang et al. (2018b) calculated the wave forces on a fixed cylinder in a multi-directional irregular wave field by the CFD model REEF3D. CFD technique has shown good performance in the simulation of 3D complex sea states, which provides opportunity for the simulation of ship motions in complex sea states.
This study conducts a comprehensive CFD numerical simulation of ship motion in cross waves. This paper is organized in a following way. In the next section, Section 2, the CFD based basic governing equations and the established numerical model and method are reported. In Section 3, the involved research conditions are determined and described. In Section 4, characteristics of cross wave are systematically analyzed by theoretical deduction and CFD simulation. The motion response behaviors of a S175 ship model in different cross wave conditions are systemically investigated in Section 5. The safe operational guidance of ship when encountering cross wave is investigated and proposed in Section 6. Main conclusions obtained from this study are summarized in Section 7.
Section snippets
Ship model description
A standard ship model of S175 containership is used for investigation in this study. Numerical modeling and calculation are conducted in model scale with a scale ratio of 1:40 which was determined to be in accordance with the CFD numerical or tank physical model of S175 containership used in a large number of references (e.g. Lakshmynarayanana and Temarel, 2020; Datta and Guedes Soares, 2020; Fonseca and Guedes Soares, 2004a; Fonseca and Guedes Soares, 2004b). The body plan of the S175 hull is
Research scheme and simulation conditions
The cross waves can be described by their two component regular waves. In this study, the frequency and amplitude of the two component regular waves are assumed to be identical and they are coming from two orthogonal directions in deep water. In order to investigate ship motion response in harsh wave conditions, the wave height of component regular wave is set at 120 mm (full-scale 4.8 m). Wave length to ship length ratio λ/L = 1.0 is selected for the majority of the cases to obtain ship
Characteristics of cross waves
In this section, the space and time distributional characteristics of cross waves are theoretically analyzed at first. Then the monitored wave elevation encountered by ship from CFD simulation are presented and analyzed.
Ship motions in cross waves
In this section, ship motion responses in cross waves are systematically analyzed. As concluded from the above analysis, the cross waves encountered by the ship are symmetrical in the Cases 1–9. Thus ship motion responses in these conditions are first analyzed due to their regularity and simplicity. Then ship asymmetrical motion responses in the Cases 10–13 are further analyzed to investigate ship motions in different wave headings.
Safe navigational strategy of ship in cross waves
According to the above analysis, the ship will probably encounter large amplitude vertical or transverse motion when sailing in cross waves. The cross waves will pose a threat to the navigational safety of ship. Therefore, it is of great importance to provide some wise strategy for the operational guidance of ship when operating in cross waves.
As concluded from Section 4.1, in the cross waves field there exist stagnation lines where the wave elevation remains zero and time-invariant. The ship
Conclusions
This paper originally investigates ship motion behavior in bi-directional cross waves by CFD tool. Some useful insight and guidance for the safety operation of ship when encountering cross seas are also provided. Main conclusions drawn in this study are as follows:
- (1)
The in situ monitored wave elevation within a cross wave field follows a mono-chromatic sine function. The frequency of the resultant waves is the same as the component regular waves, but their amplitude differs for different
CRediT authorship contribution statement
Jialong Jiao: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing, Visualization, Project administration. Songxing Huang: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Visualization. Carlos Guedes Soares: Resources, Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 51909096), the Pre-Research Field Foundation of Equipment Development Department of China (No. 61402070106), and the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515011181). The first author would also like to thank the China Scholarship Council (CSC) for the financial support of his one-year visit to CENTEC at the University of Lisbon.
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